2 Answers
2

A principle is a sort of rule, but more to govern personal behaviour. Think of it as a personal rule, one that shouldn't affect other people. A rule is generally imposed by a figure of authority, and used to guide and govern people. So in the above sentence, it would be:

Strict rules govern the clothes we wear

Because it is being imposed by someone else. If someone were to say:

That goes against my principles.

That would mean that they felt you were breaking one of their personal rules, or perhaps asking them to break a personal rule.

Rules state what is legally or procedurally correct, whereas principles state what is morally or intrinsically correct.

To address your specific example,

Strict rules govern the clothes we wear

because "strict" and "govern" both imply that an dress code is being enforced, or some fashion conventions should be adhered to (e.g., "Don't wear white after Labor Day" or "Don't wear fur or leather to a courtroom").